Title:Gaia Data Release 2: Validation of the classification of RR Lyrae and Cepheid variables with the Kepler and K2 missions

Abstract: The second data release of the Gaia mission includes an advance catalog of
variable stars. The classification of these stars are based on sparse
photometry from the first 22 months of the mission. We set out to investigate
the purity and completeness of the all-sky Gaia classification results with the
help of the continuous light curves of the observed targets from the Kepler and
K2 missions, focusing specifically on RR Lyrae and Cepheid pulsators, outside
the Galactic Bulge region. We crossmatched the Gaia identifications with the
observations collected by the Kepler space telescope. We inspected the light
curves visually, then calculated the relative Fourier coefficients and period
ratios for the single- and double-mode K2 RR Lyrae stars to further classify
them. We identified 1443 and 41 stars classified as RR Lyrae or Cepheid
variables in Gaia DR2 in the targeted observations of the two missions and 263
more RR Lyre targets in the Full-Frame Images (FFI) of the original mission. We
provide the crossmatch of these sources. We conclude that the RR Lyrae catalog
has a completeness between 70-78%, and provide a purity estimate between 92-98%
(targeted observations) with lower limits of 75% (FFI stars) and 51% (K2
worst-case scenario). The low number of Cepheids prevents us from drawing
detailed conclusions but the purity of the DR2 sample is estimated to be around
66%.